Donato Cafagna

NEW 3D-SCROLL ATTRACTORS IN HYPERCHAOTIC CHUA'S CIRCUITS FORMING A RING

This paper presents an approach for generating new hyperchaotic attractors in a ring of Chuas circuits. By taking a closed chain of three circuits and exploiting sine functions as nonlinearities, the proposed technique enables 3D-scroll attractors to be generated. In particular, the paper shows that 3D-scroll dynamics can be designed by modifying six parameters related to the circuit nonlinearities.

Hyperchaotic Coupled Chua Circuits: An Approach for Generating New n×m-Scroll Attractors

In this paper an approach for generating new hyperchaotic attractors from coupled Chua circuits is proposed. The technique, which exploits sine functions as nonlinearities, enables n×m-scroll attractors to be generated. In particular, it is shown that n×m-scroll dynamics can be easily designed by modifying four parameters related to the circuit nonlinearities. Simulation results are reported to illustrate the capability of the proposed approach.

FRACTIONAL-ORDER CHUA'S CIRCUIT: TIME-DOMAIN ANALYSIS, BIFURCATION, CHAOTIC BEHAVIOR AND TEST FOR CHAOS

In this tutorial the chaotic behavior of the fractional-order Chuas circuit is investigated from the time-domain point of view. The objective is achieved using the Adomian decomposition method, wh...

BIFURCATION AND CHAOS IN THE FRACTIONAL-ORDER CHEN SYSTEM VIA A TIME-DOMAIN APPROACH

This tutorial investigates bifurcation and chaos in the fractional-order Chen system from the time-domain point of view. The objective is achieved using the Adomian decomposition method, which allows the solution of the fractional differential equations to be written in closed form. By taking advantage of the capabilities given by the decomposition method, the paper illustrates two remarkable findings: (i) chaos exists in the fractional Chen system with order as low as 0.24, which represents the smallest value ever reported in literature for any chaotic system studied so far; (ii) it is feasible to show the occurrence of pitchfork bifurcations and period-doubling routes to chaos in the fractional Chen system, by virtue of a systematic time-domain analysis of its dynamics.

Fractional-order systems without equilibria: The first example of hyperchaos and its application to synchronization

A challenging topic in nonlinear dynamics concerns the study of fractional-order systems without equilibrium points. In particular, no paper has been published to date regarding the presence of hyperchaos in these systems. This paper aims to bridge the gap by introducing a new example of fractional-order hyperchaotic system without equilibrium points. The conducted analysis shows that hyperchaos exists in the proposed system when its order is as low as 3.84. Moreover, an interesting application of hyperchaotic synchronization to the considered fractional-order system is provided.

HYPERCHAOS IN THE FRACTIONAL-ORDER RÖSSLER SYSTEM WITH LOWEST-ORDER

This Letter analyzes the hyperchaotic dynamics of the fractional-order Rossler system from a time-domain point of view. The approach exploits the Adomian decomposition method (ADM), which generates series solution of the fractional differential equations. A remarkable finding of the Letter is that hyperchaos occurs in the fractional Rossler system with order as low as 3.12. This represents the lowest order reported in literature for any hyperchaotic system studied so far.

DECOMPOSITION METHOD FOR STUDYING SMOOTH CHUA'S EQUATION WITH APPLICATION TO HYPERCHAOTIC MULTISCROLL ATTRACTORS

This paper focuses on the numerical study of chaotic dynamics via the Adomian decomposition method. The approach, which provides series solutions of the system equations, is first applied to Chuas circuit and Chuas oscillator, both with cubic nonlinearity. Successively, the method is utilized for obtaining hyperchaotic multiscroll attractors in a ring of three Chuas circuits, where the smooth nonlinearities are Hermite interpolating polynomials. The reported examples show that the approach presents two main features, i.e. the system nonlinearity is preserved and the chaotic solution is provided in a closed form.

SYNCHRONIZATION OF HYPERCHAOTIC CIRCUITS VIA CONTINUOUS FEEDBACK CONTROL WITH APPLICATION TO SECURE COMMUNICATIONS

In this paper a synthesis technique for the synchronization of hyperchaotic circuits with application to secure communications is developed. It is well known that information-bearing signals can be considered as causes of perturbations, when a secure communication system based on a masking technique is implemented. Starting from this consideration, in this paper a feedback control scheme is developed to guarantee synchronization between transmitter and receiver. The control scheme involves as many state variables in the feedback as the number of information signals to be transmitted. After deriving the nonlinear dynamics of the synchronization error system, the feedback matrix is determined by finding a suitable Lyapunov function and by imposing the conditions which assure the global asymptotic stability of the origin of the error system. The method is illustrated by considering hyperchaotic circuits constituted by coupled Chuas oscillators, for which analytic expressions of the feedback gains are derived.

AN EFFECTIVE METHOD FOR DETECTING CHAOS IN FRACTIONAL-ORDER SYSTEMS

This paper illustrates a reliable binary test for detecting the presence of chaos in nonlinear systems described by fractional-order differential equations. The method, which is inspired by the technique proposed in [Gottwald & Melbourne, 2004] for integer-order differential equations, does not require phase space reconstruction of the fractional system. It consists of obtaining the data series, constructing a random walk-type process and studying how the variance of the random walk scales with time. In order to show the capabilities of the approach, the test is successfully applied to three well-known dynamical systems, i.e. fractional Chua, Chen and Lorenz systems.

DESIGN OF A HYPERCHAOTIC CRYPTOSYSTEM BASED ON IDENTICAL AND GENERALIZED SYNCHRONIZATION

In this paper identical and generalized synchronization and the complex dynamics of hyperchaotic circuits are exploited for designing reliable cryptosystems. Since chaotic additive masking, chaotic switching and chaotic parameter modulation methods can have a low degree of security, an attempt to overcome this drawback is made by utilizing hyperchaotic circuits which make available several chaotic signals. Some of these signals are used to properly synchronize the encrypter and the decrypter in an identical and generalized way. Other chaotic signals are considered for encrypting and decrypting the information messages by means of a multishift cipher scheme. The approach is applied to a communication system constituted by an encrypter and a decrypter each consisting of two coupled Chuas circuits, unidirectionally coupled with two coupled Chuas oscillators. Simulation results are reported to show the performance of the suggested cryptosystem.